I've been interested in Roman history as a whole, but it seems that the Eastern/Byzantine Empire does not have a whole lot of books dedicated to it. (I already have The Alexiad, which is great, if possibly biassed.)
Do any of the people here have any recomendation? I've searched around, and I might be a complete idiot, but even the Book list does not have a whole lot of books about this.
Are you looking for primary sources or secondary sources?
Procopius is the most prominent Eastern historian during the 6th century. He wrote a glowing account of Justinian, but there is also his Secret History in which he exposes all of the gritty excesses of the imperial court. There are some really good translations available and there are some free editions online if you just search.